Currently (As of Jan 31, 2012) it is possible to have immunity to both lightning and water although they are opposite elements. This is done by combining the water with either ice or fire to make steam, which can coexist with lightning, then reverting it back to water with the opposite of ice or fire you used earlier as the last element conjured. For example, [QFAER] makes Steam, Lightning, Shield, then the cold cancels the fire in steam leaving you with Water, Lightning, Shield. You cannot conjure another element after the cancel or the game will detect and eliminate your opposite pair of Water and Lightning. The most versatile shield of this type is [QFQFASER] Which grants Steam, Water, Arcane, and Lightning immunity. Why would this be useful? You can, for instance, conjure up a Thunderstorm [QFQFASA] magick and be completely immune to its effects while spamming Arcane Steam Rocks [QFSD] everywhere. You will also be dry during the Thunderstorm in case you need to conjure Lightning for any reason - perhaps to revive a party member.

P.S. Try this in the elemental section of Niflheim - The rain will instantly turn them all into water elementals, and the lightning strikes will instantly kill them.

Cast Shield (personal) to take the hit. Carry the Staff of War for extra hit points.

Cast Lightning+Shield before the Thunder Storm. Your shield will expire halfway through the storm, as Thunder Storm has a longer duration (17.5 seconds vs 12 seconds). Re-cast it by first casting Water+Shield to let you use lightning in the rain.

Carry the Righteous Rod of Runes which grants electricity immunity. However, this involves leaving your staff behind. The rod is only carried by dwarves, who occur only underground (where Thunder Storm won't work) or in the battle with Grimnir (where you'll be whisked away after you kill the dwarf).

If you're only going for the achievement, do it in singleplayer. It's easier for one player to survive the Thunderstorm.

The easiest way to survive Thunderstorm is with the Rod of righteous Runes. It grants you lightning immunity simply by carrying it.

Lightning + Shield, Self works but it usually wears off before the storm is over. You can't recast the lightning immunity because you'll be wet from the rain storm.
To get around this be sure to cast a personal shield (a good idea anyway), Shield, Self.
Or you can alternate casting water immunity then lightning immunity on yourself throughout the thunderstorm.

The EASIEST method is a permanent lightning immunity staff. During Grimnir's mind battle, the last opponent you face is a dwarf wizard who drops a "rod of righteous runes" - the permanent lightning immunity it grants would see you through a thunderstorm with ease. You can also get this staff in chapter 11 when you face them there. The downside is that its active ability is quite weak, and the broad immunity circle may make nearby opponents lit immune. If you're just going for the achievement though, this will work.

Without a staff, lightning immunity (lit + shield, self cast) DOES work - but it has two limitations.
a) It does NOT apply to your shield, dome or personal shield
b) It also fades after a few seconds, so remember to keep re-casting it. I suspect this is where you are failing - you dont notice it's gone and a late hit zaps you.